7) The output of a potentiometer is measured by a voltmeter having a resistance Rm, as...

  

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7) The output of a potentiometer is measured by a voltmeter having a resistance Rm, as shown in Figure 3.12. R, is the resistance of the total length X, of the potentiometer and R; is the resistance between the wiper and common point C for a general wiper position X;. Show that the measurement error due to the resistance R, of the measuring instrument is given by R (R, – R;) R,(R;R, + RmR – R}) Error = E Hence show that the maximum error occurs when X; is approximately equal to 2X,/3. (Hint-differentiate the error expression with respect to R; and set to 0. Note that maximum error does not occur exactly at X; = 2X,/3, but this value is very close to the position where the maximum error occurs). Figure 3.12 15) The translational motion potentiometer of Prob. 7) above has a stroke length of 200 mm and is to be used in a particular measurement situation. The output voltage from the potentiometer is to be measured by an instrument whose resistance is 15 k. The maximum measurement error, which occurs when the slider is positioned two-thirds of the way along the element (i.e., when Ri = 2R:/3 in Fig. 3.12 above), must not exceed 0.5% of the full-scale reading. The highest possible measurement sensitivity is also required. A family of potentiometers having a power rating of 0.1 W per mm and resistances ranging from 100 2 to 10 k2 in 100 2 steps are available. Choose the most suitable potentiometer from this range and calculate the measurement sensitivity that it provides. 7) The output of a potentiometer is measured by a voltmeter having a resistance Rm, as shown in Figure 3.12. R, is the resistance of the total length X, of the potentiometer and R; is the resistance between the wiper and common point C for a general wiper position X;. Show that the measurement error due to the resistance R, of the measuring instrument is given by R (R, – R;) R,(R;R, + RmR – R}) Error = E Hence show that the maximum error occurs when X; is approximately equal to 2X,/3. (Hint-differentiate the error expression with respect to R; and set to 0. Note that maximum error does not occur exactly at X; = 2X,/3, but this value is very close to the position where the maximum error occurs). Figure 3.12 15) The translational motion potentiometer of Prob. 7) above has a stroke length of 200 mm and is to be used in a particular measurement situation. The output voltage from the potentiometer is to be measured by an instrument whose resistance is 15 k. The maximum measurement error, which occurs when the slider is positioned two-thirds of the way along the element (i.e., when Ri = 2R:/3 in Fig. 3.12 above), must not exceed 0.5% of the full-scale reading. The highest possible measurement sensitivity is also required. A family of potentiometers having a power rating of 0.1 W per mm and resistances ranging from 100 2 to 10 k2 in 100 2 steps are available. Choose the most suitable potentiometer from this range and calculate the measurement sensitivity that it provides.